Academies and free schools should be forced to publish comprehensive data on the family background and parental income of all children applying and winning places, it was claimed.

The report – led by Christine Gilbert, the former head of Ofsted – said that the official admissions watchdog should be required to intervene at schools where there is evidence of a “lack of parity” between the numbers of rich and poor pupils.

It comes amid claims from researchers that some academies are “finding methods to select covertly” to tailor admissions towards well-behaved children from wealthy backgrounds.

This includes holding special social events with prospective parents, staging pre-admission meetings and requesting supplementary information on families, which are all banned by national admissions rules.

The report suggested that a rise in the number of academies and free schools, which are independent of local councils and have more freedom to control their own admissions, may fuel “social segregation”.

Official figures show that fewer than 15 per cent of pupils attending academies are from the poorest backgrounds compared with a national average of almost 17 per cent. Numbers drop as low as nine per cent in free schools, which are academy-style institutions set up by parents’ groups and charities.

The conclusions – in a study published as part of the “Academies Commission” established jointly by the Royal Society of Arts and the publisher Pearson – are likely to create fresh concerns over so-called “social engineering”, with legitimate applicants from middle-class homes being denied places.

It comes days after the Telegraph told how more than 10 pupils are applying for each place at some of the most popular academies.

Miss Gilbert, who resigned as head of Ofsted in 2011, said the “ambition and pace of the government’s academies programme cannot be doubted”.

But she added: “There has to be enough support and challenge in the system, and enough checks and balances, for academies or groups of academies to be able to use the independence they have gained professionally and with moral purpose.”

Under the last Government, academy status was reserved for the poorest performing schools. Comprehensives with a poor track record were hauled out of local authority control and placed in the hands of private sponsors with freedom over admissions, staff pay, the curriculum, length of the school day and shape of the academic year.

The Coalition has dramatically extended academy status to all schools, with around six-in-10 secondaries already converting or planning to convert.

But the study said “numerous submissions to the commission suggest some academies are finding methods to select covertly”.

In a series of key recommendations, the study said: “Academies should be required to publish comprehensive socio-economic data about who applies and who is admitted, with the Office of the Schools Adjudicator responsible for acting on suggestions of a lack of parity.”

A spokesman for the Department for Education said: “All admissions authorities – be they local councils or self-governing schools including academies – must comply with our new fair admissions code. It is clear about what they must do when admitting pupils.

“We specifically changed the law so that anyone who has concerns about how any state-funded school is admitting pupils can formally object to the Office of the Schools Adjudicator.

“This Government has also given all good schools, including academies, the freedom to take more pupils – so increasing the number of pupils who are getting a first-class education.

"Thousands of heads have chosen to take advantage of the benefits that come with academy status - they are the ones who know their pupils best, and they are now the ones in charge of their schools, free from town hall bureaucracy, and raising standards.

“We have also have expanded the sponsored academy programme so that thousands of primary school pupils will now also get the first-class education they deserve.”